CSflim

Not too sharp on my astrophysics! Just wondering, if a black hole is considered to be in a state of high or low entropy?

If you consider the maximum entropy state, with all energy uniformly distributed over a vast space, and compare it too a black hole, which is a huge amount of energy stored in a tiny space they appear to be polar opposites, which would make you come to the conclusion that a black hole is low entropy.

If you were to take a star as a closed system and watch it collapse into a black hole, surely it would stay as a black hole. If a black hole was considered a low entropy state, then it would seem to violate the second law? Unless it is possible for a black hole to "un-collapse" itself?

I am aware of Hawking radiation. Which means that a black hole can actually spew out matter. Would it be possible for it to spew out enough to destabilise it, and "de-collapse" it?
As far as I know hawking radiation works as such: (correct me if I'm wrong)
Near the "threshold of no return" of a black hole a matter/antimatter particle pair comes into existence. Normally these particles would instantly annihilate each other, but in this circumstance, one of the particles is caught by the gravity of the black hole, but the other manages to escape.
Which of the particles escapes? The particle or anti particle? And why? Surely both are under the influence of the massive gravity?

Imagining that a Big Crunch were to happen (which it seems it won't) then it would seem that it also would violate the second law, as it would presumably start off as the forming of many black holes? If this was so, surely a black hole is indeed high entropy?

The Big Bang singularity was obviously low entropy. What fundamental difference is there between this singularity and a singularity in a black hole? My only explanation is that even though the Big Bang singularity contained a huge amount of matter in a tiny space, that tiny space was in fact ALL space.

How would (in theory) the Big Crunch singularity differ from the Big Bang singularity? How does this difference ensure that the second law is not broken?

Could the Big Crunch singularity become unstable and also set off another Big Bang? To the best of my knowledge this is impossible, but could someone clarify....and why?

Anyway, hopefully you'll be able to answer my questions. Any recommendations for a good book for on astrophysics? I'm am reasonably well read on classical physics, relativity and quantum physics. This is my final frontier. *groan*

I haven't yet worked up the guts to dive into A Brief History Of Time!

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digby

You might try The Elegant Universe by Brian Greene. I thought that it was a good read.

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cowlick

wow! I have no idea what the answer is; the question is really fascinating!

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"It's a long story," says I, and let him up.

Conclamo Ludus

With the knowledge you have now, you should have no problem digesting A Brief History of Time.

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CSflim

Oh. Thats good to hear. Just I've heard quite a few horror stories of people running out to get this book, only to give up a few pages in, and having the book live out the rest of its life gathering dust on the coffee table!

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Raw Kuts

I have the audio version of A Brief History of Time and I loved it so much I bought the print version (not as well cause I didn't exactly "buy" the audio version).

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MacGnG

this is how i figure it:
entropy is disorder.
something at absolute zero would be at no (low) entropy.
a black hole would be at high entropy because it is full of disorder, but not too much to be unstable.

BentNotTwisted

CSfilm,
As far as your original question regarding Black Hole entropy, I have made an inquiry into a co-worker who is (hopefully) better versed in the subject than I. I'll let you know what she says.
Regarding the collapsing universe, I'm not sure of the answer. The most recent research in astrophysics indicates the expansion of the universe is actually speeding up. This had been happening in the last few billion years and cosmologists are at a loss to explain it. With that in mind it's doubtful there ever will be a big crunch.
My understanding of Hawking radiation is that after a black hole gives off a certain amount of matter it will succumb to a massive explosion. BTW, if you are able to understand Hawking radiation you can definitely handle A Brief History of Time. If you want something a bit less intimidating you could try Hawking's "The Universe in a Nutshell." It explains how the universe works without going into the details that overwhelm the more pedestrian reader. Not that you're pedestrian.

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IS THAT IT ???!!!
Do you even know what 'it' is?

When the last man dies for just words that he said... We Shall Be Free

BentNotTwisted

My friend referred me to this article. I'm not sure if this answers your question, but it is a fascinating read about Black Holes anyway.
http://www.sciencedaily.com/releases...0423075643.htm
Source:

Los Alamos National Laboratory

Date:

2002-04-23

Los Alamos Researcher Says "Black Holes" Aren't Holes At All
ALBUQUERQUE, N.M., April 21, 2002 - Researchers from the U.S. Department of Energy's Los Alamos National Laboratory and the University of South Carolina have provided a hypothesis that "black holes" in space are not holes at all, but instead are more akin to bubbles.

Researcher Emil Mottola of Los Alamos' Theoretical Division today presented a new explanation for black holes at the American Physical Society annual meeting in Albuquerque, N.M. Pawel Mazur of the University of South Carolina is Mottola's co-author. The researchers' explanation redefines black holes not as "holes" in space where matter and light inexplicably disappear into another dimension, but rather as spherical voids surrounded by an extremely durable form of matter never before experienced on Earth. Mazur and Mottola call the extraordinary objects Gravastars.

The Gravastar explanation for black holes helps provide answers to some of the daunting questions raised by traditional black-hole descriptions. Based on earlier-held astrophysical explanations, black holes form in space when stars reach the end of their lives and collapse in on themselves. According to black hole theory, the matter from these dying stars occupies a tiny amount of space - a mere pinpoint - and creates a mind-boggling gravitational field so powerful that nothing can escape, not even light.

Mottola and Pawel suggest that while some degree of collapsing does take place in a dying star, the collapse proceeds only to a certain point. At that point, the intense gravity of the dying star transforms the star's matter into an entirely new phase. Mottolla describes this phase as similar to a Bose-Einstein condensate, a phase of matter recently observed in a laboratory setting and the subject of scientific excitement in the past few years.

On Earth, a Bose-Einstein condensate forms when matter is plunged to very low temperatures approaching Absolute Zero, the theoretical temperature at which all atomic motion - the motion of electrons, protons and all other subatomic particles within an individual atom - is believed to cease. When matter is cooled sufficiently to become a Bose-Einstein condensate, the atoms that make up the matter enter a strange new phase. The atoms all reach the same energy state, or quantum state, and they coalesce into a blob of material called a "super atom." The properties of Bose-Einstein condensates are the subject of intense study and many physicists are working to understand them.

Mottola and Mazur believe that dying stars collapse to the "Event Horizon" - in essence the point of no return for objects entering the gravitational field of a black hole. At this point, the matter in the dying star transforms to a new state of matter that forms a Gravastar. According to the two researchers, the dying star's matter creates an ultra-thin, ultra-cold, ultra-dark shell of material that is virtually indestructible. The new form of gravitational energy in the interior is akin to a Bose-Einstien condensate, although it appears on the inside to be a bubble of vacuum, hence the term Gra (vitational) Va (cuum) Star, or Gravastar.

"Since this new form of matter is very durable, but somewhat flexible, like a bubble, anything that became trapped by its intense gravity and smashed into it would be obliterated and then assimilated into the shell of the Gravastar," Mottola said. "However, any matter in the vicinity that fell onto the surface could be re-emitted as another form of energy, which would make Gravastars potentially much more powerful emitters of radiation than black holes, which simply swallow the material."

The space trapped inside the Gravastar's shell is a similarly uncanny conceptually. The interior of the Gravastar would be totally warped space-time (the traditional three dimensions plus time). According to the researchers, this interior space would exert an outward force on the shell, adding to its durability.

Although unconventional, Mottola and Mazur's Gravastar explanation for black holes does solve at least one serious quandary created by black hole theory. Under a black-hole scenario, the amount of entropy created in a black hole would become nearly infinite. Physicists have struggled for years to account for the huge entropy of black holes, and largely have failed. Unlike their black hole counterparts, Gravastars would have a very low entropy.

Mottola and Mazur continue to refine their theory and are working on a concept behind rotating Gravastars. They even suggest that the universe we now know and live in may be the interior of a Gravastar.

"These are fascinating concepts to think about," Mottola said. "I look forward to exploring this hypothesis further."

Los Alamos National Laboratory is operated by the University of California for the U.S. Department of Energy.

For more Los Alamos news releases, visit World Wide Web site http://www.lanl.gov/external/news/releases

Editor's Note: The original news release can be found here.

This story has been adapted from a news release issued by Los Alamos National Laboratory.

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IS THAT IT ???!!!
Do you even know what 'it' is?

When the last man dies for just words that he said... We Shall Be Free

telekinetic2

No way, dig in...I took it out in like five hours in the jaccuzzi on vacation. It's a real easy read...just because he's a brain doesn't mean you have to be to understand his stuff. Part of his massive intelligence is his ability to interpret for the masses.

BRS

I think entropy depends on a subjective vantage point, i.e. what do you consider to be orderly and disorderly? So in one sense, it is both and neither.

hobo

BentNotTwisted has a good article. If things go well for those guys, Gravastars might replace Black Holes. Too bad that won't happen until I'm out of school.

Scorpion23

Scientific American had an article a few months ago that dealt with the theoretical information capacity of a Black Hole. It also touched upon the subject of entropy and the event horizon. I know that SA isn't a very technical publication but it has some useful information about the general subject.
"Information in the Holographic Universe"
http://scientificamerican.com/articl...89EEDF&catID=2

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David2000

Forget a brief history of time--it's not very well written and needlessly confusing. I've read nearly every book mentioned in this post and the best one i've read is Hyperspace by Michio Kaku. You won't put it down.

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CSflim

Since I posted this thread, I've read A Brief History of Time, and The Universe in a Nutshell. I thought they were quite good, but a bit too "anecdotal", and often didn't bother to explain many of the concepts involved.

Hyperspace has now been added to my "reading queue". Thanks.

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stingc

Black holes have very very high entropy. There are lots of ways to calculate this, and none of them are all that rigorous, but they all give the same answer (so it seems right). This is a very complicated subject, so I'll only be able to scratch the surface.

The usual intuitive argument starts with looking at what the "state variables" are for a black hole. A static classical gas for example is described by pressure, density, and temperature at equilibrium. These are the only things that are measurable classically, so they define the "state" of the system. Now thinking in terms of molecules, there is not just one configuration that corresponds to a measured pressure, density, temp. There are many microscopic configurations corresponding to a single classical state. Counting this degeneracy gives entropy. A large number of microstates for a given classical state means high entropy. This is usually how entropy is defined. It is only occasionally related to "disorder!"

Anyways, there is a remarkable theorem in general relativity stating that a stationary black hole is completely described by three parameters - mass, angular momentum, and electric charge. A black hole must have some quantum mechanical structure, but nobody really knows what this is since there isn't any good theory of quantum gravity (not molecules this time). It doesn't matter for this argument though. There is some unknown fine structure that has to be there. It could be quantized spacetime "chunks," strings or whatever. Its possible to go to string theory for example, and figure out how many string configurations correspond to a given classical mass, ang mom, and charge, just like I talked about above with gases. This is anything but intuitive. You can get an idea of the same thing by figuring out how many (classical) initial states of a system end up in the same final state.

The initial state of a black hole should be a normal star. Say its in equilibrium. How many parameters describe it? You again have total mass, angular momentum, and charge, but these things can be distributed throughout the star in many ways. It also has different types of matter in different places etc. It takes a lot of information to describe a star even classically. Eventually the star blows up and collapses into a black hole if it is large enough. Now how many different stars will collapse to a black hole with a given mass, ang. momentum, and charge? Since a star has so many parameters associated with it, and a black hole so few, you'd expect a huge number of different types of stars to collapse to the same hole. This implies a large entropy.

(I'm ignoring the not insignificant "state" of ejected matter and radiation from a supernova, but I'm trying to brief)

stingc

A black hole emits Hawking radiation, which is energy, and therefore mass. The mass is taken away from the black hole, so it gets smaller over time. The rate at which it gets smaller increases the smaller it gets, so its kind of like a runaway reaction. Nobody knows if the black hole ever disappears entirely. It eventually gets small enough that quantum gravity is required to describe what's going on.

This has been the popular line of how Hawking radiation works for over 20 years, but the usual calculations have nothing to do with particle/antiparticle pairs. There's no good intuitive picture for them actually.

Then a couple of years ago someone decided to see if this cartoon picture actually made any sense in reality. Amazingly, it all worked out. This is a valid way of looking at it. (just thought I'd clarify the history)

Anyways, both the particle and antiparticle have an equal probability to escape.

As for your other questions, the answers are mostly that nobody knows. First of all, things are really messed up and nonintuitive in standard classical relativity. Almost every notion from classical physics is thrown out the window. Its therefore very difficult to define what entropy and the 2nd law even mean except in the most idealized situations.

Add to that that entropy is best defined (not the only way though) by comparing microstates and macrostates. Nobody has much of an idea what microstates are in curved spacetime because there's no quantum gravity theory.

Also, singularities are problems with the classical theory. Understanding them will require a quantum description.

stingc

I have one last rant about this. Black holes may not exist in the sense that everyone thinks of them.

Relativity is very very hard to work with. Einstein's equations have only been solved in a couple of simple cases. The first of these solutions was in fact the simplest black hole. It was perfectly spherically symmetric, static, and in perfect vacuum exccept at its exact center. Generalizations were eventually found to rotating and electrically charged holes, but there were still stationary, isolated, and in vacuum almost everywhere.

These solutions are very interesting to play with, and are widely studied because its so hard to do anything else. Most of the things we say we "know" about black holes come from these solutions. But it has to be asked whether its reasonable to assume that just because these things could exist that they actually do. Assume that the universe didn't start with these things. Then we say a star collapses to form one. There's been a lot of work trying to show that this actually happens, but what I've seen of it is not entirely convincing.

It ignores cosmology for example. There are some tricks done whereby an infinite amount of time measured by one observer is finite to another. After "infinite time," however that may be defined, I think the external universe could have an influence. On top of that, Hawking radiation is supposed to be happening etc. The leap from collapsing star to black hole with singularity is a massive one.

If you've ever taken a physics course in high school or college, you've dealt with singularities. Except we call them "point charges," or "point masses" in Newtonian physics. Just because they solve the equations doesn't mean they exist. (Actually, a complete classical description does not allow point charges, but that's a whole other discussion. Nobody has been able to transfer the relevant arguments to GR anyway.)

CSflim

Wow, thanks stingc for the posts. Very informative.

Just one question, which I am still a bit unclear about:
Would a Big Crunch break the second law?

Ignore the fact that, at the moment, it appears a Big Crunch will not actually happen...if it did, would it go against the second law?
Surely if the universe was to contract, its density would cause the creation of black holes, and then these black holes would merge to form bigger black holes, until eventually we were left with nothing but one "huge" black hole, being the final singularity of the universe. Since you said that black holes are very high entropy, then it would not break the second law.
But what fundamental difference is there to a huge black hole singularity, and the big bang singularity?
Am I completely misguided in comparing the two?

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stingc

I don't know. I've never seen any work on that. Its probably been discussed somewhere though.

wry1

I will say this: if the Gravastar theory pans out, then we will know that it is fundamentally possible to lase matter - as that is what is being described when the article discusses all matter making up the shell of the Gravastar as having the same Quantum state.

Interesting indeed!